Advanced Design Technique (Multidisciplinary Optimization [Engineering])

PART A: Set up an objective function for your design project and identify the constraints involved. Prepare a presentation slide and a short write-up.

PART B: Minimize f(x) = x sin x

Check what happens if x = 1.0769 at any point during the search.

1) Find the solution using Newton's method.

Start from the initial bound points x₀ = -0.5 & x₀ =1.5

Decide when x^* has converged, note the number of function iterations & function evaluations.

Count each calculation f, f' or f" as one function evaluation.

2) Find the solution using Golden Section method.

Start from initial bound points x_L= -0.5 and x_U = 1.5

Decide when x^* has converged, note the number of function iterations & function evaluations.

Count each calculation f, f' or f" as one function evaluation.

3) Compare the number of iterations & function evaluations required by Newton's method to the number required by the Golden Section.